Bale ran 50 yards and beat four Liverpool players before setting up Aaron Lennon for Tottenham's first and then beat Pepe Reina with a brilliant 30-yard free-kick to double the hosts' lead.
The fact that Bale signed a new contract last summer has not stopped Barcelona and Real Madrid being heavily linked with the 23-year-old, and Villas-Boas admits he may be powerless to stop the winger leaving.
"At the moment he is performing extremely well for Spurs and we are amazed at what he can do for us. He is on to a great career," Villas-Boas said. "Obviously Tottenham as a football club want to keep him here for as long as we can but we understand players like this have propositions and a market, which is the nature of the game."
Should either of the Spanish giants have had scouts at Wednesday night's game at White Hart Lane, they will have been impressed with Bale's outstanding performance.
His pace, creativity and finishing were sublime throughout the game - with the only negative point coming in the second half when he got in the way of Lennon's clearance, which struck his head and went in to his own net.